Absolute convergence of Fourier integrals and Lipschitz classes

B.I. Peleshenko (Dnipropetrovsk State Agrarian and Economic University)


The necessary and sufficient conditions, in terms of Fourier transforms $$$\hat{f}$$$ of functions $$$f \in L^1(\mathbb{R})$$$, are obtained for $$$f$$$ to belong to the Lipschitz classes $$$H^{\omega}(\mathbb{R})$$$ and $$$h^{\omega}(\mathbb{R})$$$.


Fourier transform; Fourier integral; modulus of continuity; Lipschitz classes


Stein I., Weiss G. Introduction to Fourier analysis on Euclidean spaces, Mir, Moscow, 1974; 333 p. (in Russian)

Moricz F. "Absolutely convergent Fourier integrals and classical function spaces", Arch. Math., 2008; 91: pp. 49-62. doi:10.1007/s00013-008-2626-8


  • There are currently no refbacks.

Copyright (c) 2011 B.I. Peleshenko

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Registered in

ISSN (Online): 2664-5009
ISSN (Print): 2664-4991